You can see the two intermediates “Let’s Encrypt Authority X3 (IdenTrust cross-signed)” and “Let’s Encrypt Authority X3 (Signed by ISRG Root X1)” there:
If I understand correctly, these two intermediate are generated using the same data (same public-private key pair, same name, etc). The only difference is one is signed by “ISRG Root X1” and the other by IdenTrust.
So to answer your question, after your generate your intermediate signed by your “Root Certificate Nr. 1”, to generate the cross signed, you just generate the exact same intermediate, but you sign it using “Root CA Nr. 2” this time.
May I ask why you want to cross signed? It’s done usually when one root is not yet trusted enough, the intermediate is cross signed by another root, which is already trusted by more devices.